Anasazi::SVQBOrthoManager< ScalarType, MV, OP > Class Template Reference

An implementation of the Anasazi::MatOrthoManager that performs orthogonalization using the SVQB iterative orthogonalization technique described by Stathapoulos and Wu. More...

#include <AnasaziSVQBOrthoManager.hpp>

Inheritance diagram for Anasazi::SVQBOrthoManager< ScalarType, MV, OP >:

Anasazi::MatOrthoManager< ScalarType, MV, OP > Anasazi::OrthoManager< ScalarType, MV > List of all members.

Public Member Functions

Constructor/Destructor
 SVQBOrthoManager (Teuchos::RefCountPtr< const OP > Op=Teuchos::null, bool debug=false)
 Constructor specifying re-orthogonalization tolerance.
 ~SVQBOrthoManager ()
 Destructor.
Orthogonalization methods
void project (MV &X, Teuchos::RefCountPtr< MV > MX, Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::Array< Teuchos::RefCountPtr< const MV > > Q) const
 Given a list of (mutually and internally) orthonormal bases Q, this method takes a multivector X and projects it onto the space orthogonal to the individual Q[i], optionally returning the coefficients of X for the individual Q[i]. All of this is done with respect to the inner product innerProd().
void project (MV &X, Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::Array< Teuchos::RefCountPtr< const MV > > Q) const
 This method calls project(X,Teuchos::null,C,Q); see documentation for that function.
int normalize (MV &X, Teuchos::RefCountPtr< MV > MX, Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > B) const
 This method takes a multivector X and attempts to compute an orthonormal basis for $colspan(X)$, with respect to innerProd().
int normalize (MV &X, Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > B) const
 This method calls normalize(X,Teuchos::null,B); see documentation for that function.
int projectAndNormalize (MV &X, Teuchos::RefCountPtr< MV > MX, Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > B, Teuchos::Array< Teuchos::RefCountPtr< const MV > > Q) const
 Given a set of bases Q[i] and a multivector X, this method computes an orthonormal basis for $colspan(X) - \sum_i colspan(Q[i])$.
int projectAndNormalize (MV &X, Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > B, Teuchos::Array< Teuchos::RefCountPtr< const MV > > Q) const
 This method calls projectAndNormalize(X,Teuchos::null,C,B,Q); see documentation for that function.
Error methods
Teuchos::ScalarTraits< ScalarType
>::magnitudeType 
orthonormError (const MV &X) const
 This method computes the error in orthonormality of a multivector, measured as the Frobenius norm of the difference innerProd(X,Y) - I.
Teuchos::ScalarTraits< ScalarType
>::magnitudeType 
orthonormError (const MV &X, Teuchos::RefCountPtr< const MV > MX) const
 This method computes the error in orthonormality of a multivector, measured as the Frobenius norm of the difference innerProd(X,Y) - I. The method has the option of exploiting a caller-provided MX.
Teuchos::ScalarTraits< ScalarType
>::magnitudeType 
orthogError (const MV &X1, const MV &X2) const
 This method computes the error in orthogonality of two multivectors, measured as the Frobenius norm of innerProd(X,Y).
Teuchos::ScalarTraits< ScalarType
>::magnitudeType 
orthogError (const MV &X1, Teuchos::RefCountPtr< const MV > MX1, const MV &X2) const
 This method computes the error in orthogonality of two multivectors, measured as the Frobenius norm of innerProd(X,Y). The method has the option of exploiting a caller-provided MX.

Detailed Description

template<class ScalarType, class MV, class OP>
class Anasazi::SVQBOrthoManager< ScalarType, MV, OP >

An implementation of the Anasazi::MatOrthoManager that performs orthogonalization using the SVQB iterative orthogonalization technique described by Stathapoulos and Wu.

Author:
Chris Baker, Ulrich Hetmaniuk, Rich Lehoucq, and Heidi Thornquist

Definition at line 54 of file AnasaziSVQBOrthoManager.hpp.


Constructor & Destructor Documentation

template<class ScalarType, class MV, class OP>
Anasazi::SVQBOrthoManager< ScalarType, MV, OP >::SVQBOrthoManager Teuchos::RefCountPtr< const OP >  Op = Teuchos::null,
bool  debug = false
 

Constructor specifying re-orthogonalization tolerance.

Definition at line 261 of file AnasaziSVQBOrthoManager.hpp.

template<class ScalarType, class MV, class OP>
Anasazi::SVQBOrthoManager< ScalarType, MV, OP >::~SVQBOrthoManager  )  [inline]
 

Destructor.

Definition at line 75 of file AnasaziSVQBOrthoManager.hpp.


Member Function Documentation

template<class ScalarType, class MV, class OP>
void Anasazi::SVQBOrthoManager< ScalarType, MV, OP >::project MV &  X,
Teuchos::RefCountPtr< MV >  MX,
Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > >  C,
Teuchos::Array< Teuchos::RefCountPtr< const MV > >  Q
const [virtual]
 

Given a list of (mutually and internally) orthonormal bases Q, this method takes a multivector X and projects it onto the space orthogonal to the individual Q[i], optionally returning the coefficients of X for the individual Q[i]. All of this is done with respect to the inner product innerProd().

After calling this routine, X will be orthogonal to each of the Q[i].

Parameters:
X [in/out] The multivector to be modified. On output, X will be orthogonal to Q[i] with respect to innerProd().
MX [in/out] The image of X under the specified operator Op. If MX != 0: On input, this is expected to be consistent with X. On output, this is updated consistent with updates to X. If MX == 0 or Op == 0: MX is not referenced.
C [out] The coefficients of X in the *Q[i], with respect to innerProd(). If C[i] is a non-null pointer and *C[i] matches the dimensions of X and *Q[i], then the coefficients computed during the orthogonalization routine will be stored in the matrix *C[i]. If C[i] is a non-null pointer whose size does not match the dimensions of X and *Q[i], then a std::invalid_argument exception will be thrown. Otherwise, if C.size() < i or C[i] is a null pointer, then the orthogonalization manager will declare storage for the coefficients and the user will not have access to them.
Q [in] A list of multivector bases specifying the subspaces to be orthogonalized against. Each Q[i] is assumed to have orthonormal columns, and the Q[i] are assumed to be mutually orthogonal.

Implements Anasazi::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 329 of file AnasaziSVQBOrthoManager.hpp.

template<class ScalarType, class MV, class OP>
void Anasazi::SVQBOrthoManager< ScalarType, MV, OP >::project MV &  X,
Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > >  C,
Teuchos::Array< Teuchos::RefCountPtr< const MV > >  Q
const [inline, virtual]
 

This method calls project(X,Teuchos::null,C,Q); see documentation for that function.

Reimplemented from Anasazi::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 113 of file AnasaziSVQBOrthoManager.hpp.

template<class ScalarType, class MV, class OP>
int Anasazi::SVQBOrthoManager< ScalarType, MV, OP >::normalize MV &  X,
Teuchos::RefCountPtr< MV >  MX,
Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > >  B
const [virtual]
 

This method takes a multivector X and attempts to compute an orthonormal basis for $colspan(X)$, with respect to innerProd().

The method does not compute an upper triangular coefficient matrix B.

This routine returns an integer rank stating the rank of the computed basis. If X does not have full rank and the normalize() routine does not attempt to augment the subspace, then rank may be smaller than the number of columns in X. In this case, only the first rank columns of output X and first rank rows of B will be valid.

The method attempts to find a basis with dimension the same as the number of columns in X. It does this by augmenting linearly dependant vectors in X with random directions. A finite number of these attempts will be made; therefore, it is possible that the dimension of the computed basis is less than the number of vectors in X.

Parameters:
X [in/out] The multivector to the modified. On output, X will have some number of orthonormal columns (with respect to innerProd()).
MX [in/out] The image of X under the specified operator Op. If $ MX != 0$: On input, this is expected to be consistent with X. On output, this is updated consistent with updates to X. If $ MX == 0$ or $ Op == 0$: MX is not referenced.
B [out] The coefficients of X in the computed basis. If B is a non-null pointer and *B has appropriate dimensions, then the coefficients computed during the orthogonalization routine will be stored in the matrix *B. If B is a non-null pointer whose size does not match the dimensions of X, then a std::invalid_argument exception will be thrown. Otherwise, the orthogonalization manager will declare storage for the coefficients and the user will not have access to them. This matrix will not be triangular in general.
Returns:
Rank of the basis computed by this method.

Implements Anasazi::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 317 of file AnasaziSVQBOrthoManager.hpp.

template<class ScalarType, class MV, class OP>
int Anasazi::SVQBOrthoManager< ScalarType, MV, OP >::normalize MV &  X,
Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > >  B
const [inline, virtual]
 

This method calls normalize(X,Teuchos::null,B); see documentation for that function.

Reimplemented from Anasazi::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 153 of file AnasaziSVQBOrthoManager.hpp.

template<class ScalarType, class MV, class OP>
int Anasazi::SVQBOrthoManager< ScalarType, MV, OP >::projectAndNormalize MV &  X,
Teuchos::RefCountPtr< MV >  MX,
Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > >  C,
Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > >  B,
Teuchos::Array< Teuchos::RefCountPtr< const MV > >  Q
const [virtual]
 

Given a set of bases Q[i] and a multivector X, this method computes an orthonormal basis for $colspan(X) - \sum_i colspan(Q[i])$.

This routine returns an integer rank stating the rank of the computed basis. If the subspace $colspan(X) - \sum_i colspan(Q[i])$ does not have dimension as large as the number of columns of X and the orthogonalization manager doe not attempt to augment the subspace, then rank may be smaller than the number of columns of X. In this case, only the first rank columns of output X and first rank rows of B will be valid.

The method attempts to find a basis with dimension the same as the number of columns in X. It does this by augmenting linearly dependant vectors with random directions. A finite number of these attempts will be made; therefore, it is possible that the dimension of the computed basis is less than the number of vectors in X.

Parameters:
X [in/out] The multivector to the modified. On output, the relevant rows of X will be orthogonal to the Q[i] and will have orthonormal columns (with respect to innerProd()).
MX [in/out] The image of X under the operator Op. If $ MX != 0$: On input, this is expected to be consistent with X. On output, this is updated consistent with updates to X. If $ MX == 0$ or $ Op == 0$: MX is not referenced.
C [out] The coefficients of the original X in the *Q[i], with respect to innerProd(). If C[i] is a non-null pointer and *C[i] matches the dimensions of X and *Q[i], then the coefficients computed during the orthogonalization routine will be stored in the matrix *C[i]. If C[i] is a non-null pointer whose size does not match the dimensions of X and *Q[i], then a std::invalid_argument exception will be thrown. Otherwise, if C.size() < i or C[i] is a null pointer, then the orthogonalization manager will declare storage for the coefficients and the user will not have access to them.
B [out] The coefficients of X in the computed basis. If B is a non-null pointer and *B has appropriate dimensions, then the coefficients computed during the orthogonalization routine will be stored in the matrix *B. If B is a non-null pointer whose size does not match the dimensions of X, then a std::invalid_argument exception will be thrown. Otherwise, the orthogonalization manager will declare storage for the coefficients and the user will not have access to them. This matrix will not be triangular in general.
Q [in] A list of multivector bases specifying the subspaces to be orthogonalized against. Each Q[i] is assumed to have orthonormal columns, and the Q[i] are assumed to be mutually orthogonal.
Returns:
Rank of the basis computed by this method.

Implements Anasazi::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 303 of file AnasaziSVQBOrthoManager.hpp.

template<class ScalarType, class MV, class OP>
int Anasazi::SVQBOrthoManager< ScalarType, MV, OP >::projectAndNormalize MV &  X,
Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > >  C,
Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > >  B,
Teuchos::Array< Teuchos::RefCountPtr< const MV > >  Q
const [inline, virtual]
 

This method calls projectAndNormalize(X,Teuchos::null,C,B,Q); see documentation for that function.

Reimplemented from Anasazi::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 200 of file AnasaziSVQBOrthoManager.hpp.

template<class ScalarType, class MV, class OP>
Teuchos::ScalarTraits<ScalarType>::magnitudeType Anasazi::SVQBOrthoManager< ScalarType, MV, OP >::orthonormError const MV &  X  )  const [inline, virtual]
 

This method computes the error in orthonormality of a multivector, measured as the Frobenius norm of the difference innerProd(X,Y) - I.

Reimplemented from Anasazi::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 216 of file AnasaziSVQBOrthoManager.hpp.

template<class ScalarType, class MV, class OP>
Teuchos::ScalarTraits< ScalarType >::magnitudeType Anasazi::SVQBOrthoManager< ScalarType, MV, OP >::orthonormError const MV &  X,
Teuchos::RefCountPtr< const MV >  MX
const [virtual]
 

This method computes the error in orthonormality of a multivector, measured as the Frobenius norm of the difference innerProd(X,Y) - I. The method has the option of exploiting a caller-provided MX.

Implements Anasazi::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 276 of file AnasaziSVQBOrthoManager.hpp.

template<class ScalarType, class MV, class OP>
Teuchos::ScalarTraits<ScalarType>::magnitudeType Anasazi::SVQBOrthoManager< ScalarType, MV, OP >::orthogError const MV &  X1,
const MV &  X2
const [inline, virtual]
 

This method computes the error in orthogonality of two multivectors, measured as the Frobenius norm of innerProd(X,Y).

Reimplemented from Anasazi::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 231 of file AnasaziSVQBOrthoManager.hpp.

template<class ScalarType, class MV, class OP>
Teuchos::ScalarTraits< ScalarType >::magnitudeType Anasazi::SVQBOrthoManager< ScalarType, MV, OP >::orthogError const MV &  X1,
Teuchos::RefCountPtr< const MV >  MX1,
const MV &  X2
const [virtual]
 

This method computes the error in orthogonality of two multivectors, measured as the Frobenius norm of innerProd(X,Y). The method has the option of exploiting a caller-provided MX.

Implements Anasazi::MatOrthoManager< ScalarType, MV, OP >.

Definition at line 291 of file AnasaziSVQBOrthoManager.hpp.


The documentation for this class was generated from the following file:
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